Question: U.S. News and World Report (19 December 1994, pp. 62-71) reported on a survey of 1000 American adults, conducted by telephone on December 2-4, 1994, designed to measure beliefs about apocalyptic predictions. They reported that the margin of error was "3 percentage points."
a. Verify that the margin of error for a sample of size 1000 is as reported.
b. One of the results reported was that 59% of Americans believe the world will come to an end. Construct a 95% confidence interval for the true percentage of Americans with that belief, using the margin of error given in the article. Interpret the interval in a way that could be understood by a statistically naive reader.